camera image not rendering
Problem

This behavior is because Object Data > Background Images only shows the image in the viewport -- there is no physical image. An easy workaround uses compositing.

Workaround

First, go to the Render tab > Film dropdown and check Transparent. This will tell Blender to only render the cube as opposed to the cube and the gray background.

Next, switch from the Layout layout to the Compositing layout. Add an Input > Image node and use the bottom left button to select your image (it has already been added to your .blend file, so it should be there).

Add a Distort > Scale node and connect the Image node > Image output to the Scale node > Image input. Set the Scale node > dropdown to Render Size. Add a Color > Alpha Over node and connect the Scale node > Image output to the top Alpha Over node > Image input. Connect the Render Layers node > Image output to the bottom Alpha Over node > Image input. Connect the Alpha Over node > Image output to the Composite node > Image input. Your nodes should now look like this:



Render.